It is well known that the use of multiple antennas at the transmitter and/or receiver may significantly boost the performance of a wireless system. Multi-antenna techniques can significantly increase the data rates and reliability of a wireless communication system. If both the transmitter and the receiver are equipped with multiple antennas, the result is a multiple-input multiple-output, MIMO, communication channel. Such systems and/or related techniques are commonly referred to as MIMO.
Multi-antenna configurations such as MIMO have the potential of both improving data rates and increasing diversity. Precoding is an example of a multi-antenna technique for improving the performance of a wireless information transferring system by transforming the information carrying transmit vector so that the vector better fits the channel conditions. This may be performed based on channel information or completely without channel information or some combination thereof. Often, precoding is implemented as performing a linear transformation on the information carrying vector prior to transmission. Such linear transformation is usually represented by a matrix. Precoding is an integral part of 3GPP Long Term Evolution, LTE, as well as of Wideband Code Division Multiple Access, WCDMA, and Worldwide Interoperability for Microwave Access, WiMax.
There are two basic types of precoding: codebook based and non-codebook based. Codebook based precoding involves the precoding matrix implementing the linear transformation being selected from a countable and typically finite set of candidate matrices. The set of candidate matrices constitutes the codebook. On the other hand, non-codebook based precoding does not involve any quantization. The precoding element may thus for example be a continuous function of the channel matrix.
Beamforming is a special case of the more general notion of precoding and involves a single information carrying symbol stream being multiplied by a channel dependent vector that adjusts the phase of the signal on each transmit antenna so that coherent addition of the transmit signals is obtained at the receiver side. This provides diversity as well as increases the Signal-to-Noise Ratio (SNR). The precoder matrix may need to be signaled, by means of feedback signaling and/or signaling of the chosen precoder element in the forward link. The feedback signaling may be viewed as a way for the receiver to provide channel information to the transmitter.
Several different approaches are known for implementing such forward link signaling. For codebook based precoding, explicit signaling of the precoder element index in the forward link is possible. The precoder may also be implicitly signaled using precoded pilots/reference symbols/reference signals, RS, that together with non-precoded reference symbols may be used at the receiver to determine the used precoder element. Another possibility is to use precoded reference symbols also for the demodulation of the data, that is, to use so-called dedicated RS or alternatively demodulation RS or UE specific RS, and absorb the precoder element into the effective channel from the perspective of the receiver.
As mentioned above, the precoder may be determined/selected with different levels of information of the propagation channel between the transmitter and the receiver. Precoder selection that does not rely on the channel state is often referred to as open-loop precoding and is particularly useful in scenarios where the channel state changes rapidly and is not possible to track with sufficient precision. In more stationary scenarios, closed-loop precoding performs significantly better, because the precoder is adaptively selected to match the state of the channel and thereby maximize the performance.
Closed-loop precoding relies on the availability of channel state information at the transmitter, which must be provided by a feedback mechanism from the receiver. Such feedback may be analogue in the form of sounding signals in the reverse link or digitally signaled over a reverse link. For example, the receiver may select or recommend a precoder (or precoders) from a precoder codebook and feed back the corresponding codebook index to the transmitter, e.g. as in Rel-8 of LTE and which is referred to as implicit feedback in some contexts. A precoder recommendation may be seen as a form of channel quantization since typically a set of channel realizations map to a certain precoding element.
Current closed loop MIMO systems where a precoding codebook is used for channel feedback are built on the assumption that there is a phase difference between two antenna elements which value is strictly the same between any two nearby antennas in a linear equally spaced antenna array. The value of the phase difference determines the beam pointing direction of the resulting beam. This is reflected in the codebook of precoding vectors in e.g. LTE, where the precoding vectors are taken from columns in Discrete Fourier Transform, DFT, matrices.
Ideally, the DFT vector model matches the principal eigenvector to the MIMO channel and maximal antenna gain can be achieved. In reality however, there will be a mismatch between the DFT based codebook and real MIMO channels because of several reasons:                The channel is not perfectly line of sight, it has an angular spread and the DFT vector is therefore not matched to the true channel, i.e. the principal eigenvector has not DFT vector structure and precoding gain is lost. The strict linear and equal phase progression relationship between adjacent antennas is thus subject to phase relaxation.        The DFT based codebook has a finite set of beam pointing directions and if a UE is positioned in between two existing beam main directions there is a loss in precoding gain.        The hardware in the transmitter does not have an identical phase for all the transmit antennas. One reason for this phase relaxation is that cable lengths and so forth from the transmitter to the actual antenna element are different for different antennas. This will defocus the main beam and have the effect that precoding gain is reduced.        The hardware in the transmitter does not have an identical time delay for all antennas. This would cause a frequency dependent beam pointing offset compared to the ideal beam pointing direction.        
In TDD systems or in FDD systems using beamforming, reciprocity can be used to reduce feedback overhead. In such systems, both the receive and transmit chains typically have to be calibrated such that uplink measurements can be used to determine downlink precoding. In this case, errors in the receive chain calibration can also cause incorrect precoding matrices to be used for the downlink.
Hence, there is inefficiency in the current codebook design due to these circumstances, which is a problem that leads to reduced antenna gain and increased interference in the system.